With the development of networked systems, logical dynamic system (LDS) has attracted a lot of attentions due to its wide background in biological system, economical system, social system etc [1]}, [2]}, [3]}. Two representative application fields of LDS are Boolean networks [1]} and networked evolutionary games [5]}.
LDSs investigate the logic evolutionary dynamics on graphs [6]}. The appeal of LDS is that it merges the interactions between nodes and the evolutionary dynamics of nodes together, which makes it a theoretically valued model [7]}.
